The largest interval lying in $\left( - \frac { \pi } { 2 } , \frac { \pi } { 2 } \right)$ for which the function $\left[ f ( x ) = 4 ^ { - x ^ { 2 } } + \cos ^ { - 1 } \left( \frac { x } { 2 } - 1 \right) + \log ( \cos x ) \right]$ is defined, is\\
(1) $[ 0 , \pi ]$\\
(2) $\left( - \frac { \pi } { 2 } , \frac { \pi } { 2 } \right)$\\
(3) $\left[ - \frac { \pi } { 4 } , \frac { \pi } { 2 } \right)$\\
(4) $\left[ 0 , \frac { \pi } { 2 } \right)$